Sure! Solving ratio problems using proportions involves setting up a relationship between two ratios and then solving for an unknown value. Here’s the step-by-step method for solving such problems:
Steps to Solve Ratio Problems Using Proportions
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Identify the Ratios: Determine the two ratios that are given in the problem.
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Set Up a Proportion: Write the two ratios as a fraction and set them equal to each other.
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Cross Multiply: This step involves multiplying across the equals sign to create an equation.
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Solve for the Unknown: Isolate the variable and solve for it.
Example Problem 1
Problem: If 3 apples cost $1.50, how much do 5 apples cost?
Step 1: Identify the Ratios
- Ratio of apples to cost: \( 3 \text{ apples} : 1.50 \text{ dollars} \)
Step 2: Set Up the Proportion Let \( x \) be the cost of 5 apples. \[ \frac{3 \text{ apples}}{1.50 \text{ dollars}} = \frac{5 \text{ apples}}{x \text{ dollars}} \]
Step 3: Cross Multiply \[ 3x = 1.50 \times 5 \] \[ 3x = 7.50 \]
Step 4: Solve for the Unknown \[ x = \frac{7.50}{3} = 2.50 \] Thus, 5 apples cost $2.50.
Example Problem 2
Problem: A recipe requires a ratio of 2 cups of flour to 3 cups of sugar. If you want to use 4 cups of flour, how much sugar do you need?
Step 1: Identify the Ratios
- Ratio of flour to sugar: \( 2 \text{ cups flour} : 3 \text{ cups sugar} \)
Step 2: Set Up the Proportion Let \( y \) be the amount of sugar needed when using 4 cups of flour. \[ \frac{2 \text{ cups flour}}{3 \text{ cups sugar}} = \frac{4 \text{ cups flour}}{y \text{ cups sugar}} \]
Step 3: Cross Multiply \[ 2y = 3 \times 4 \] \[ 2y = 12 \]
Step 4: Solve for the Unknown \[ y = \frac{12}{2} = 6 \] Thus, you need 6 cups of sugar when using 4 cups of flour.
Summary
- Identify ratios and set up a proportion.
- Cross multiply to form an equation.
- Solve for the unknown variable.
If you have a specific problem in mind, feel free to share it, and I can help you solve it!
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